Anterior Cruciate Ligament (ACL) rupture is one of the commonest injuries in sports medicine. However, the rates of the reported graft re-rupture range from 2–10%, leading to around 3000 to 10000 revision ACL reconstructions in United States per annum. Inaccurate tunnel positions are considered to be one of the commonest reasons leading to failure and subsequent revision surgery. Additionally, there remains no consensus of the optimal position for ACL reconstructions.

The positions of the bone tunnels in patients receiving ACL reconstruction are traditionally assessed using X-rays. It is well known that conventional X-ray is not a precise tool in assessing tunnel positions. Thus, there is a recent trend in using three-dimensional (3D) CT. However, routine CT carries a major disadvantage in terms of significant radiation hazard. In addition, it is both inconvenient and expensive to use CT as a regular assessment tools during the follow-up.

The goal of the present work is to develop a novel 2D-3D registration method using single X-ray image and a surface model. By performing such registration for two post-operative X-rays, we can further calculate the 3D tunnel positions after ACL reconstructions. Our framework consists of five parts: (1) a surface model of the knee, (2) a 2D-3D registration algorithm, (3) a 3D tunnel position calculation, (4) a graphic user interface (GUI), and (5) a semi-transparency rendering. Among them, the crucial part is our 2D-3D registration method that estimates the relative position of the knee model in the imaging coordinate system. Once registered, the 3D position of an ACL tunnel in the knee model is calculated from the imaging geometry. The only interaction required is to mark the ACL tunnels on the X-rays through the GUI.

We propose two 2D-3D registration methods. One is a contour-based method that uses pure geometric information. Most methods in this category accomplish the registration by extracting contours in X-rays, establishing their correspondences on the 3D model, and calculating the registration parameters. Unlike these methods, which need point-to-point correspondences, our method optimises the registration parameters in a statistical inference framework without giving or establishing point-to-point correspondences. Due to the use of the statistical inference, our method is robust to the spurs and broken contours that automatically extracted by the contour detector.

The second method takes into account both the geometric shape of the object and the intensity property (intensity changes) of the image, where the intensity changes can be detected via image gradients. The use of gradient is based on the interpretation that two images are considered similar, if intensity changes occur at the same locations. The angles between the image gradients and the projected surface normals were used as a distance measure. The summation of the measures for all projected model points gives us the gradient term, which we multiply the contour-based measurement. Multiplication is preferred over addition because addition of the terms would require both terms to be normalised.

To evaluate the feasibility of our methods, a simulation study was conducted using Digitally Reconstructed Radiographs (DRR) of a sawbone underwent a single-bundle ACL reconstruction performed by an experienced orthopedic surgeon. The real position of the bone tunnel entry point was obtained using the CT images, which were acquired using a custom-made well-calibrated cone-beam CT. The knee model was built by downsampling and smoothing the high-resolution CT reconstructions. It is important in our experiments to make the model different from the original reconstruction since this simulates the condition in which patient's CT is unavailable. Two DRRs generated from approximately anteroposterior and lateral viewpoints were used. For each DRR, 50 trials of 2D-3D registration were carried out for the femoral part using 50 different initialisations, which were randomly selected from the values independently and uniformly distributed within ±10 degrees and ±10 mm of the ground-truth.

Compared with the ground-truth established using the CT images, our single image contour-based method achieved accurate estimations in rotations and in-plane translations, which were (−0.67±1.38, −0.98±0.84, −0.42±0.71) degrees and (0.11±0.26, −0.06±1.20) mm for the anteroposterior image, and (−0.78±0.76, −0.37±0.87, 0.70±0.88) degrees and (−0.14±0.22, 0.31±0.71) mm for the lateral one, respectively. The same experiments were also performed using the second method. However, it did not produce desirable results in our experiments. The tunnel entry point was then calculated using the averaged registration result of our contour-based method. The entry point of the tunnel was obtained with high accuracy of 1.25 mm distance error from the real position of the entry point.

For the 2D-3D registration, the estimated off-plane translations showed relatively low accuracy. It is well known that the depth can be difficult to be accurately estimated using one single image. As the result showed, the accuracy in rotations and in-plane translations is more important for ACL tunnel position estimation in our framework. As for the image gradient, it is too sensitive to the small perturbation caused by image noises. A more robust way of integrating the gradient information into our contour-based method is required. We propose a novel approach for estimating the 3D position of bone tunnels in ACL reconstruction using two post-operative X-rays. It was tested in a sawbone study using DRRs. The most significant advantage of our approach is to potentially eliminate the necessity of acquiring a patient's CT. The success in developing and validating the proposed workflow will allow convenient and precise assessment of tunnel positions in ACL reconstruction with minimal risk of radiation hazard.